Natural characteristic and vibration analysis of nonlinear articulated multi-beam ring structure for modeling ring truss antenna under base excitation

Abstract

The investigation of natural characteristic and dynamic response of the ring truss antenna is essential for its design and vibration control since its high flexibility and nonlinearity. This paper investigates the dynamic properties of the articulated multi-beam ring structure for modeling the ring truss antenna under base excitation. The mathematical model of the multi-beam ring structure is established based on the global mode method. The matching conditions of force and displacement at connected points and boundary conditions of the ring structure are obtained. The global mode method and separation of variables method are applied to derive the analytical characteristic equation. Then natural frequency and global mode of the system are obtained. The orthogonality of global modes is proved. Based on the Galerkin procedure, the global modes which are explicitly functions are truncated to be substituted into the nonlinear partial differential equations of the system to yield the low dimensional discrete dynamic model with high accuracy described by ODEs which is useful for designing active vibration controllers. Afterwards the validity of the dynamic model is verified by comparing natural frequencies and mode shapes with those obtained by FEM. Finally, the effects of system parameters including external excitation, linear stiffness, third-order nonlinear stiffness, damping and friction torque on natural characteristic and dynamic response for the first resonance are analyzed. The results show that parameters of the structure have a significant effect on the whole system. The dynamic analysis in the paper is meaningful for design and vibration control of the antenna for the future study.